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在数学命题中包含着条件与结论,我们解题要得到正确的结论,前提是明确命题中全部基本条件,由于问题中的条件有的是明列的,有的是隐含的,因而降低条件的隐含仕,提高挖掘隐含条件的本领是很重要的.为此本文讨论条件隐含的相对性以及我们对隐含条件的对策. 一、条件隐含的相对性我们先来讨论几个例子. 例1 试求f(x)=aresin(x~2-x+1)~(1/2)的值域. 对这个问题在同一个年级里的学生会给出如下四种不同的解答: 1)仅考虑到反正弦函数的值域,给出[-π/2,π/2]的结论;
In mathematics propositions contain conditions and conclusions, we solve the problem to get the correct conclusions, the premise is to define all the basic conditions in the propositions, because the conditions in the problem are clearly listed, and some are implied, thus implying the conditions implied It is very important to improve the ability to mine implicit conditions. For this reason, we discuss the implicit nature of conditions and our countermeasures for implied conditions. First, the conditional implied relativity. Let’s discuss a few examples. Example 1 Try to find the range of f(x)=aresin(x~2-x+1)~(1/2). There are four different answers to this question for students in the same grade: 1) Only consider To the domain of the inverse sine function, give the conclusion of [-π/2, π/2];